YES! If you want to use public transportation, you must buy a ticket before you board
the bus, tram or trolleybus. You need to purchase a two-zone ticket for zones 100+101 for any stop in the city of Brno. Single journey tickets can be bought from machines (coins only at most with a few, including those at the main station able to take credit cards) at many stops, or in Tabak stores.
You need to validate
the single journey ticket in the Yellow validation machine when you enter the bus, tram or trolleybus. Instructions how to pay for transportation in Brno can be found here
The DPMB also offers sms tickets
. This service is only available for Czech SIM cards. To use the service, send a message with a code to 90206. The code for a 75-minute ticket (CZK 29) is BRNO. The code, BRNOD, is for an all-day ticket (CZK 99). After sending the message, you will receive a ticket via SMS within a few minutes.
If you are staying in Brno for several days, consider buying a 5-day ticket which costs 250 CZK. There are several places where you can buy this ticket, but the easiest one is probably the main train station. You can buy it at any counter (look for the international counters because they are more likely to speak English). When you first use your ticket, be sure to validate it. You only have to validate your ticket one time.